Problem: Rewrite as a simplified fraction. ${1.3\overline{59} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1359.5959...\\ 10x &= 13.5959...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1346}$ ${x = \dfrac{1346}{990}} $ ${x = \dfrac{673}{495}} \text{or} {1 \dfrac{178}{495}}$